Homotopy analysis Sumudu transform method for time--fractional third order dispersive partial differential equation

TL;DR: In this article, a mixture of the Laplace transformation and homotopy perturbation technique is used to solve fractional-order Whitham-Broer-Kaup equations.

TL;DR: In this study, an applicable and effective method, which is based on a least-squares residual power series method (LSRPSM), is proposed to solve the time-fractional differential equations.

TL;DR: In this paper, under the non-singular fractional operator with exponential decay kernel, the Ambartsumian equation was analyzed qualitatively and computationally, and the convergence of the series solution to an exact solution was proved through nonlinear analysis.

TL;DR: In this article, a novel approach to numerical solution of a class of fourth-order time fractional partial differential equations (PDEs) is presented, where the finite difference formulation has been used for temporal discretization, whereas the space discretisation is achieved by means of non-polynomial quintic spline method.

TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.

TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.

TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.